Bookcover of Algebraic Curves in Multiple-View Geometry
Booktitle:

Algebraic Curves in Multiple-View Geometry

An algebraic geometry approach to computer vision

LAP LAMBERT Academic Publishing (2011-12-08 )

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ISBN-13:

978-3-8454-2132-2

ISBN-10:
3845421320
EAN:
9783845421322
Book language:
English
Blurb/Shorttext:
We introduce multiple-view geometry for algebraic curves,with applications in both static and dynamic scenes. More precisely, we show how the epipolar geometry can be recovered from algebraic curves. For that purpose, we introduce a generalization of Kruppa’s equations, which express the epipolar constraint for algebraic curves. Reconstruction from a single image based on symmetry is also considered and we show how this relates to algebraic curves for a simple example. We also investigate the question of three-dimensional reconstruction of an algebraic curve from two or more views. In the case of two views, we show that for a generic situation, there are two solutions for the reconstruction, which allows extracting the right solution, provided the degree of the curve is greater or equal to 3. When more than two views are available,we show that there construction can be done by linear computations, using either the dual curve or the variety of intersecting lines. In both cases, no curve fitting is necessary in the image space. Finally we focus on dynamic scenes and show when and how the trajectory of a moving point can be recovered from a moving camera.
Publishing house:
LAP LAMBERT Academic Publishing
Website:
https://www.lap-publishing.com/
By (author) :
Jeremy-Yrmeyahu Kaminski
Number of pages:
92
Published on:
2011-12-08
Stock:
Available
Category:
Geometry
Price:
49.00 €
Keywords:
Algebraic Curves, Multiple-View Geometry

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